We have investigated the dynamics of magnetic domain walls in three epitaxial garnet films with g values of 1.07, 4.8, and ≳30, and having wall mobilities of 880, 930, and 820 cm/sec Oe, respectively. Bubble collapse measurements in the films with g=1.07 and 4.8 showed velocity saturation with the approximate values 1500 and 8000 cm/sec, respectively. The film with g≳30 showed no saturation, and velocities up to 6×104 cm/sec were observed. These results are consistent with the expected increase in the Slonczewski and Walker critical velocities with increasing g value. Large g values make it possible to operate magnetic bubble circuits at higher frequencies than is otherwise the case.